Solitary Waves In Fluids

Edited by R.H.J. Grimshaw, this book covers the topic of solitary waves in fluids.

This is the first thorough examination of weakly nonlocal solitary waves, which are just as important in applications as their classical counterparts. The book describes a class of waves that radiate away from the core of the disturbance but are nevertheless very long-lived nonlinear disturbances.

Since the first description by John Scott Russel in 1834, the solitary wave phenomenon has attracted considerable interests from scientists. The most interesting discovery since then has been the ability to integrate most of the nonlinear wave equations which govern solitary waves, from the Korteweg-de Vries equation to the nonlinear Schrodinger equation, in the 1960's. From that moment, a huge amount of theoretical works can be found on solitary waves. Due to the fact that many physical phenomena can be described by a soliton model, applications have followed each other, in telecommunications

Non-linear behaviour of water waves has recently drawn much attention of scientists and engineers in the fields of oceanography, applied mathematics, coastal engineering, ocean engineering, naval architecture, and others. The IUTAM Symposium on Non-linear Water Waves was organized with the aim of bringing together researchers who are actively studying non-linear water waves from various viewpoints. The papers contained in this book are related to the generation and deformation of non-linear water waves and the non-linear interaction between waves and bodies. That is, various types of non-linear water waves were analyzed on the basis of various well-known equations, experimental studies on breaking waves were presented, and numerical studies of calculating second-order non-linear wave-body interaction were proposed.

Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.

The dynamics of flows in density-stratified fluids has been and remains now an important topic for scientific enquiry. Such flows arise in many contexts, ranging from industrial settings to the oceanic and atmospheric environments. It is the latter topic which is the focus of this book. Both the ocean and atmosphere are characterised by the basic vertical density stratification, and this feature can affect the dynamics on all scales ranging from the micro-scale to the planetary scale. The aim of this book is to provide a “state-of-the-art” account of stratified flows as they are relevant to the ocean and atmosphere with a primary focus on meso-scale phenomena; that is, on phenomena whose time and space scales are such that the density stratification is a dominant effect, so that frictional and diffusive effects on the one hand and the effects of the earth’s rotation on the other hand can be regarded as of less importance. This in turn leads to an emphasis on internal waves.

This book presents selected articles from the International Conference on Asian and Pacific Coasts (APAC 2019), an event intended to promote academic and technical exchange on coastal related studies, including coastal engineering and coastal environmental problems, among Asian and Pacific countries/regions. APAC is jointly supported by the Chinese Ocean Engineering Society (COES), the Coastal Engineering Committee of the Japan Society of Civil Engineers (JSCE), and the Korean Society of Coastal and Ocean Engineers (KSCOE). APAC is jointly supported by the Chinese Ocean Engineering Society (COES), the Coastal Engineering Committee of the Japan Society of Civil Engineers (JSCE), and the Korean Society of Coastal and Ocean Engineers (KSCOE).